WASHINGTON — President Trump is expected to formally sign off on imposing stiff tariffs on steel and aluminum imports at noon on Thursday, according to people familiar with the deliberations, although advisers close to the White House emphasized that the timing could change.

The tariffs would not go into effect immediately, however, with a two-week implementation period required under the statute that gives the president authority to impose the measures. That could give countries or companies a chance to submit input and try to sway the administration’s plan, according to the people familiar with the deliberations.

Mr. Trump has said the tariffs would apply to all countries across the board and that any exemptions could open a Pandora’s box of requests. But he and other administration officials have also indicated that Canada, Mexico or other close allies could be exempted through renegotiated trade deals or other measures.

The swiftness with which the administration plans to formally announce the tariffs comes on the heels of Gary D. Cohn’s announcement on Tuesday that he will resign as Mr. Trump’s top economic adviser. Mr. Cohn has been among the most ardent free trade supporters in the White House and has argued the tariffs will start a global trade war that will hurt the United States economy.

The prospect of approaching tariffs has tipped off furious lobbying from governments around the world, who have tried to sway the administration with offers of friendship and threats of retaliation. On Wednesday, the European Union released a list of American-made goods it would penalize if the tariffs went through.

In a surprise announcement last Thursday, Mr. Trump told steel and aluminum executives gathered at the White House that he intended to place tariffs of 25 percent on imported steel and 10 percent on imported aluminum.

The signing would fulfill a key campaign promise for the president, and it has garnered support from metal companies, unions and Rust Belt politicians. United States Steel Corporation announced Wednesday that it planned to reopen a blast furnace at a plant in Granite City, Ill. to support increased demand for American steel they expected as a result of the tariff.

But it has sparked fierce opposition from foreign governments, industries that use steel and aluminum in their products and national security advisers who have warned that the measure could risk alienating allies.